Delay dependent robust stability of singular systems with additive time-varying delays

This paper considers the problem of delay-dependent robust stability for uncertain singular systems with additive time-varying delays. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The results are expressed in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.     

Stabilization of controlled positive discrete‐time T‐S fuzzy systems by state feedback control

This paper deals with sufficient conditions of asymptotic stability and stabilization for nonlinear discrete‐time systems represented by a Takagi–Sugeno‐type fuzzy model whose state variables take only nonnegative values at all times t for any nonnegative initial state. This class of systems is called positive systems. The conditions of stabilizability are obtained with state feedback control. This work is based on multiple Lyapunov functions. The results are presented in linear matrix inequalities form. A real plant is studied to illustrate this technique. Copyright © 2010 John Wiley & Sons, Ltd.     

Regulator problem for linear continuous-time delay systems withnonsymmetrical constrained control

The regulator problem is studied for linear continuous-time delay systems with nonsymmetrical constrained control. Necessary and sufficient conditions allowing the autors to obtain the largest nonsymmetrical polyhedral positively invariant with respect to (w.r.t.) the system in the closed loop are given, The case of symmetrical constrained control is obtained as a particular case     

Comments on “Delay independent robust stability of uncertain linear systems”

The purpose of this note is to give a counterexample to a possible implication of the main result of the above paper [1].     

Stabilisation of controlled positive delayed continuous-time systems

This article solves the stabilisation problem by output feedback control for linear continuous-time systems with delay. This technique can be applied for both positive systems and controlled positive systems (systems becoming positive in closed-loop). The synthesis of feedback controllers is solved in terms of linear programs, extending the solution also to stabilisation with bounded control and stabilisation by controllers with the memory of the delayed state. The proposed conditions do not involve the value of the delay. Some examples illustrate the proposed approach.     

Full and reduced-order H∞ filtering of Takagi–Sugeno fuzzy time-varying delay systems: Input–output approach

This article addresses the issue of delay-dependent H_∞ filtering design for TakagiŮSugeno fuzzy time-varying delay systems using the input–output approach. A three-term approximation model has been used to transform the original system into two interconnected subsystems. Since the nonquadratic Lyapunov–Krasovskii functional requires to deal with the membership function's (MF) time derivative, upper-bound inequalities have been added to the obtained conditions. Based on the scaled small gain theorem, nonquadratic Lyapunov–Krasovskii functional approach and considering the bounds of the MF time-derivative, the H_∞ full- and reduced-order filters are designed and then formulated in terms of linear matrix inequalities. Finally, illustrative examples are presented to demonstrate the validity of the proposed methods.     

Robust H∞ filtering for 2D continuous systems with finite frequency specifications

This paper investigates the design problem of robust H_∞ filtering for uncertain two-dimensional (2D) continuous systems described by Roesser model with polytopic uncertainties and frequency domain specifications. Our aim is to design a new filter guaranteeing an H_∞ performance level in specific finite frequency (FF) domains. Using the well-known generalised Kalman Yakubovich Popov lemma and homogeneous polynomially parameter-dependent matrices of arbitrary degrees, sufficient conditions for the existence of H_∞ filters for different FF ranges are proposed and then unified in terms of solving a set of linear matrix inequalities. Illustrative examples are provided to show the usefulness and potential of the proposed results.     

Robust H_{\infty } filtering for uncertain two-dimensional continuous systems with time-varying delays

This paper deals with the problem of delay-dependent robust $H_{\infty }$ H ∞ filtering for uncertain two-dimensional (2-D) continuous systems described by Roesser state space model with time-varying delays, with the uncertain parameters assumed to be of polytopic type. A sufficient condition for $H_{\infty }$ H ∞ noise attenuation is derived in terms of linear matrix inequalities, so a robust $H_{\infty }$ H ∞ filter can be obtained by solving a convex optimization problem. Finally, some examples are provided to illustrate the effectiveness of the proposed methodology.